You will need to remove any loose paint then prime with a good interior primer. This is a lot of scrubbing but it has to be done. You could use a nylon scrub pad and warm/hot water to help remove the loose paint faster.
Now that you know that paint alone isn't enough, plan on priming your glazed walls before painting.
Old latex or acrylic paints can be painted over with the same type of paint without priming. The only time that priming becomes necessary is painting over old gloss latex with a lower sheen. The shiny paint is a bit too slick and needs the help of a good primer.
Also, oil based glaze and some acrylic glazes are very slick and will require priming. Keep this in your mind, when in doubt prime. You can't go wrong with priming even when it turns out to be unnecessary.